why does log a + log b = log (ab)

Let log a be some number A and log b be some number B

now the natural log of something is the equivalent of saying a=e^A and b = e^B

So a*b = e^A * e^B which by rules of indices

 = e^(A+B)

Therefore log(ab) = log(e^(A+B))

= A + B = log a + log b 

RV
Answered by Rebecca V. Maths tutor

4887 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the first derivative of y=5z(1+2z2)? Is this a minimum, maximum or turning point?


solve the equation 2cos x=3tan x, for 0°<x<360°


a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)


Solve the equation 3x^2/3 + x^1/3 − 2 = 0


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning